burgers

Location: http://people.sc.fsu.edu/~jburkardt/classes/math1091_2020/burgers/burgers.html

burgers, considers methods for the solution of the Burgers equation a nonlinear version of the advection equation.

The notes:

• burgers.pdf
• burgers.tex

Useful codes:

• expansion_wave.m,
• gaussian_wave.m, used as an initial condition for our exercises.
• shock_wave.m,
• spike_wave.m,

Exercises: Look at these after you have tried to do the work on your own.

• exercise1.m, the upwind method on BNI, the Burgers nonconservative inviscid equation.
• exercise1.png, a plot of the BNI upwind solution at the last timestep.
• exercise2.m, same as exercise1.m, but now includes a final plot of the conservation of velocity.
• exercise2.png, a plot of the BNI upwind solution at the last timestep (same as exercise1.png).
• exercise2_conservation.png, a plot of the integral ( u dx ) over time for BNI upwind.
• exercise3.m, the Lax-Friedrichs method on BNI, the Burgers nonconservative inviscid equation.
• exercise3.png, a plot of the BNI Lax-Friedichs solution at the last timestep.
• exercise3_conservation.png, a plot of the integral ( u dx ) over time for BNI Lax-Friedrichs.
• exercise4.m, simultaneously computes and plots the upwind and Lax-Friedrichs approximations to the BNI equation.
• exercise4.png, a plot of the BNI upwind and Lax-Friedichs solutions at the last timestep, with spatial resolution nx=161.
• exercise5.m, the upwind method on BCI, the Burgers conservative inviscid equation.
• exercise5.png, a plot of the BCI upwind solution at the last timestep.
• exercise5_conservation.png, a plot of the integral ( u dx ) over time for BCI upwind.

Homework: My version posted after you have turned yours in.

• hw7.m, uses a parabolic method on BCV, the Burgers Conservative Viscous equation.
• hw7.png, the solution at the last time step.
• hw7_conservation.png, a plot of the integral ( u dx ) for BCV parabolic.

Images:

• gaussian_wave.png, a plot of the Gaussian curve used for the initial condition of several exercises.
• pileup.png, a three-car pileup.